Yes, one can still get the flu after getting a flu shot. This may be because there are other respiratory viruses like rhinoviruses while the flu vaccine only protects against influenza, not other illnesses.
Another explanation may be that the person may have been exposed to the influenza viruses, which cause the flu, shortly before getting vaccinated or during the two-week period after vaccination that it takes the body to develop immune protection.
The person may also have been exposed to a flu virus different from the viruses the vaccine is designed to protect against.
Does flu vaccine increase coronavirus risk?
An article published on some websites and several Facebook posts claimed that the flu vaccine increases the risk of coronavirus infection. The U.S. Centers for Disease Control and Prevention has addressed this issue saying that the “preponderance of evidence suggests that this is not a common or regular occurrence and that influenza vaccination does not, in fact, make people more susceptible to other respiratory infections.”